where \(\Delta =16\) , \(b\)  is a gauge-invariant impact parameter, and \(V^{\prime }(r)=dV(r)/dr\) . The first two terms give the correct classical values reported in Eq.(REF ) whereas, the last term is a quantum gravity effect of order \(G_N^2\hbar m/b^3= \ell _p^2 r_s/(2b^3)\) . Our result is different from the one given in Eq.(12) of [1]}, and in Eq.(5.45) of [2]}, as expected from the analysis done in Sec.REF , in particular:
